Issue 41

A. Mardaliazad et alii, Frattura ed Integrità Strutturale, 41 (2017) 504-523; DOI: 10.3221/IGF-ESIS.41.62 519 The hexagonal constant stress elements are used for all the solid parts. The automatic penalty-based formulation contacts are considered for all the components and the static friction coefficient is set to 0.4. In the LS-DYNA model, instead of applying single point constraints to the SPH particles, which can lead to inaccurate results and numerical instabilities, specific boundary conditions at the symmetry planes were imposed [39]. The BOUNDARY_SPH_SYMMETRY_PLANE keyword creates automatically an imaginary plane which reflects the forces of a set of ghost particles to the particles in the model. Although these ghost particles have identical properties as the real ones, they do not physically exist and simply contribute to the particle approximation [21]. Figure 13 : Distribution of numerical stresses in the X direction (along the length); (a) KCC model; (b) LDP model. The maximum principal strain is considered as the eroding criteria for FEM to SPH particles conversion for all the numerical simulations. The numerical results of KCC and LDP models in terms of stress distribution along length are shown in Fig. 13a and b, respectively. Fig. 13 represents the distribution of the X stress (along the length of specimen) one time step before failure. The tensile and the compressive stresses at both numerical models are present in the element below and above the neutral axis, respectively. However, the amount of maximum stresses in the two models are different. This issue is discussed in next chapter by comparison of the numerical results with the experimental ones. C OMPARISON OF THE NUMERICAL RESULTS WITH EXPERIMENTAL DATA he load-displacement diagrams of the numerical models; developed by the KCC (both the automatic input generation mode and the calibrated mode) and the LDP material models are compared to the experimental results according to Fig. 14 and Tab. 9. There is a row in Tab. 9, labeled as “95% CI” of experimental average value, that was also reported in Tab. 1. As previous described there is a probability of 95% that the average value of a set of populations lie inside this interval. Therefore, they can be considered a reasonable description of the physical phenomena thus suitable for comparing the numerical results. The KCC material model shows the best response compared to the others, since the reported values of all three parameters, i.e. Maximum load, Maximum displacement and Flexural strength, lie within the 95% Confidence Interval of the average value. As expected, the results obtained by the automatic input mode of the KCC model are not in good agreement with the experimental data. This issue is more critical in the displacement level, and the flexural strength is very close to the minimum value reported as 95% Confidence Interval. LDP predicts the flexural strength as 16.25 MPa which is far from the reported 95% Confidence Interval (with an overestimation of about 80% respect to the experimental average value). Therefore, it is not reliable to model the mechanical behaviour of Pietra Serena in case of a significant tensile stress is present. Indeed, the Drucker-Prager criterion is well suitable to model the linear dependence of the material strength with p . The material behaviour of rocks, for negative values of p , deviates from linearity and the material failure points lie below the Drucker-Prager failure line leading to the overestimation of the flexural strength of the material. The numerical results obtained by the full calibrated mode of KCC, on the other hand, show significant agreement with the experimental data. By recalling the fact that this material model is T (a) (b)